ALL INDIA TEST SERIES

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1 From Long Term Classroom Programs and Medium / Short Classroom Program 4 in Top 10, 10 in Top 0, 43 in Top 100, 75 in Top 00, 159 in Top 500 Ranks & 354 t o t a l s e l e c t i o n s i n I I T - J E E 0 1 FIITJEE JEE (Main), 013 ALL INDIA TEST SERIES CNCEPT RECAPITULATIN TEST (Set IV) Time Allotted: 3 Hours Maximum Marks: 43 Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose. You are not allowed to leave the Examination Hall before the end of the test. INSTRUCTINS A. General Instructions 1. Attempt ALL the questions. Answers have to be marked on the MR sheets.. This question paper contains Three Parts. 3. Part-I is Physics, Part-II is Chemistry and Part-III is Mathematics. 4. Each part has only one section: Section-A. 5. Rough spaces are provided for rough work inside the question paper. No additional sheets will be provided for rough work. 6. Blank Papers, clip boards, log tables, slide rule, calculator, cellular phones, pagers and electronic devices, in any form, are not allowed. B. Filling of MR Sheet 1. Ensure matching of MR sheet with the Question paper before you start marking your answers on MR sheet.. n the MR sheet, darken the appropriate bubble with black pen for each character of your Enrolment No. and write your Name, Test Centre and other details at the designated places. 3. MR sheet contains alphabets, numerals & special characters for marking answers. C. Marking Scheme For All Three Parts. (i) Section-A (01 to 0 and 09 to 30) contains 4 multiple choice questions which have only one correct answer. Each question carries +4 marks for correct answer and 1 mark for wrong answer. Section-A (03 to 08) contains 6 multiple choice questions which have only one correct answer. Each question carries +8 marks for correct answer and mark for wrong answer. Name of the Candidate Enrolment No. FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi , Ph , , Fax

2 AITS-CRT(Set-IV)-PCM-JEE(Main)/13 Useful Data PHYSICS Acceleration due to gravity g = 10 m/s Planck constant h = J-s Charge of electron e = C Mass of electron m e = kg Permittivity of free space ε 0 = C /N-m Density of water ρ water = 10 3 kg/m 3 Atmospheric pressure P a = 10 5 N/m Gas constant R = J K 1 mol 1 CHEMISTRY Gas Constant R = J K 1 mol 1 = Lit atm K 1 mol 1 = Cal K 1 mol 1 Avogadro's Number N a = Planck s constant h = J s = erg s 1 Faraday = coulomb 1 calorie = 4. joule 1 amu = kg 1 ev = J Atomic No: H=1, He =, Li=3, Be=4, B=5, C=6, N=7, =8, N=9, Na=11, Mg=1, Si=14, Al=13, P=15, S=16, Cl=17, Ar=18, K =19, Ca=0, Cr=4, Mn=5, Fe=6, Co=7, Ni=8, Cu = 9, Zn=30, As=33, Br=35, Ag=47, Sn=50, I=53, Xe=54, Ba=56, Pb=8, U=9. Atomic masses: H=1, He=4, Li=7, Be=9, B=11, C=1, N=14, =16, F=19, Na=3, Mg=4, Al = 7, Si=8, P=31, S=3, Cl=35.5, K=39, Ca=40, Cr=5, Mn=55, Fe=56, Co=59, Ni=58.7, Cu=63.5, Zn=65.4, As=75, Br=80, Ag=108, Sn=118.7, I=17, Xe=131, Ba=137, Pb=07, U=38. FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi , Ph , , Fax

3 3 AITS-CRT(Set-IV)-PCM-JEE(Main)/13 Physics PART I SECTIN A Single Correct Choice Type This section contains 30 multiple choice questions. Each question has four choices,, and (D) out of which NLY NE is correct. 1. In the LCR circuit, the voltmeter and ammeter readings are 00 volt, 0A 00 volt, 50A 1000 volt, 0A (D) 1000 volt, 0A A V 400V 400V C 50Ω L 1000V, 50 Hz ~. A collision occurs between two identical balls each of mass m, moving with velocities u 1 and u, colliding head-on. The coefficient of restitution is 0.5. The energy lost in the collision is 1 mu ( ) 1 + u 1 mu ( ) 1 u mu ( 1 u ) (D) mu ( 1 u ) In the figure shown, the ammeter reads a current equal to R R V R 3 V R V R V (D) R V R A R R R R FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi , Ph , , Fax

4 AITS-CRT(Set-IV)-PCM-JEE(Main)/ From A conducting sphere of radius R a cavity of radius R/ is cut out as shown in the figure. At the centre of cavity a point charge q is placed then the field and potential at point P as shown in the figure is P d R q R/ q q V =, E = πε d πε d 0 0 q q V =, E = 4πε d 4πε d 0 0 q q V =, E = 4πε d πε d 0 0 q q (D) V =, E = πε d 4πε d The switch Sw of the circuit shown in the figure is closed at t = 0. i 1 and i are the electric current in the branch containing two ideal inductors L 1 and L respectively, at a certain instant. Choose the most appropriate statement. di1 At t = 0,(just after the switch is closed) ε di ε = and = dt L1 dt L At t = 0,,(just after the switch is closed) i 1 = 0, i = 0 εl εl1 After long time i1 = andi = (L1+ L )r (L1+ L )r (D) All the above L 1 L ε r Sw 6. A conical flask of mass 10 kg and base area as 10 3 cm is floating in liquid of relative density 1., as shown in the figure. The force that liquid exerts on curved surface of conical flask will be (Given g = 10 m/s ) 0 N downward direction 40 N in downward direction can be determined only if θ is given (D) 0 N in upward direction θ 10cm FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi , Ph , , Fax

5 5 AITS-CRT(Set-IV)-PCM-JEE(Main)/13 7. Potential difference across a resistance is measured as V = (0 ±.01) volts and current flowing through it is measured as i = (1 ±.01) A. Then the value of resistance measured by hm s law R = V/i is (0 ± 1.) Ω (0 ± 0.8) Ω (0 ± 1) Ω (D) (0 ± 0.6) Ω. 8. A tunnel is made inside earth passing through center of earth. A particle is dropped from the surface of earth. Select the correct statement Kinetic energy of particle is maximum at center and its potential energy is zero at center velocity of particle is proportional to x [where x is distance of particle from center of earth Kinetic energy of particle is maximum when it reaches on the other side of tunnel. (D) kinetic energy of particle is maximum at center m 9. The time period of a pendulum at temperature t 1 ºC is T 1 sec. Its time period at t ºC is T sec. If coefficient of linear expansion of material of pendulum is α, then increase in time period is α(t t 1 ) α(t t 1 )/3 T 1 α(t t 1 )/ (D) none of these 10. A graph between the temperature read on the Celsius Scale and that on the Fahrenheit Scale, when plotted, gives the following: ºC ºC ºF ºF ºC ºC (D) ºF ºF FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi , Ph , , Fax

6 AITS-CRT(Set-IV)-PCM-JEE(Main)/ A particle moving in the positive x-direction has initial velocity v 0. The particle undergoes retardation kv, where v is its instantaneous velocity. The velocity of the particle as a function of time is given by v0 v = v 0 /(1 + kv 0 t) v = 1+ kt v0 v v = (D) v = 0 kt 1+ k v t ( ) 1. A ray of light travelling along the positive z axis is reflected twice : (i) for the first time, by a mirror whose normal is along (i ˆ + k) ˆ (ii) for the second time, by a mirror whose normal is along (i ˆ + ˆ j + k) ˆ, where the symbols have their usual meanings. The final ray is along ˆ j+ k ˆ k ˆ + ˆ i j ˆ+ kˆ ˆi (D) (j ˆ+ kˆ i) ˆ In the system shown, the acceleration of the wedge of mass 5M is (there is no friction anywhere) zero g/ g/3 (D) g/4 M 5M 60 o M 14. Two wires are placed at (, 0, 0) and (-, 0, 0) carrying equal currents along negative z-axis. Magnetic field at point (0,, 0) is along positive x-axis negative y-axis positive y-axis (D) negative z-axis FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi , Ph , , Fax

7 7 AITS-CRT(Set-IV)-PCM-JEE(Main)/ In which of the following transitions will the wavelength be minimum? n = 5 to n = 4 n = 4 to n = 3 n = 3 to n = (D) n = to n = The angular momentum of electron in an orbit is quantized because it is in accordance with particle nature of electron in accordance with wave nature compatibility of electron in accordance with Hund s rule (D) in accordance with Maxwell s theory 17. A point object is placed between two plane mirrors as shown in figure. If object is moved toward M 1 with speed u then relative speed between first images of M 1 and M is Zero u u (D) u 18. A solid cylinder of mass m length l and area of cross section A is placed as shown in the figure. If Young s modulus is Y then strain energy stored in the cylinder is mgl mgl 3AY 6AY mgl mgl (D) AY AY. M 1 10mm M L 19. A rectangular block has a square base measuring a a, and its height is h. It moves on a horizontal surface in a direction perpendicular to one of the edges of the base. The coefficient of friction is µ. It will topple if (choose the most appropriate option) µ> a/h µ > a / h µ> a/h (D) µ > h/a FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi , Ph , , Fax

8 AITS-CRT(Set-IV)-PCM-JEE(Main)/ A block of mass m is connected to two springs of spring constant k and 3k respectively, such that the spring of spring constant k is compressed by 3l when the block is in its mean position. If the block is displaced slightly and allowed to oscillate, the frequency will be 1 k π m 1 5k π 6m 1 6k π 5m (D) none of these fixed wall k smooth m fixed wall 3k π 1. A wave y1 = Asin x 4t+ is superposed with a second waveform producing a standing 3 wave with a node at x = 0. In the equation of the waveform, x is in metre and t is in second. The equation of the second waveform is y = Asin( 4t x π /3) y = Asin(x + 4t + 5 π /3) y = Asin(x + 4t 5 π /3) (D) y = Asin( x + 4t π /3). yi ˆ+ xj ˆ. A force F = b N(b is a constant) acts on a particle as it undergoes counterclockwise x + y circular motion in a circle: x + y = 16. The work done by the force when the particle undergoes one complete revolution is (x, y are in m) Zero π bj bj (D) None of these. 3. The natural frequency of the circuit shown in the figure is (Assume that equal currents i, i exist in the two branches, and the charges on the capacitors are equal) π LC π 3LC 1 1 (D) none of the above π LC i L q + C L q + C i L FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi , Ph , , Fax

9 9 AITS-CRT(Set-IV)-PCM-JEE(Main)/13 4. A block of mass m slides down an inclined wedge of same m shown in the figure. Friction is absent everywhere. Magnitude of acceleration of center of mass of the block and wedge is gsin θ zero (1+ sin θ) gcos θ gsinθ (D) (1+ sin θ) (1+ cos θ) m m θ 5. In the figure shown, if Galvanometer shows no deflection then the value of x is 4 Ω 3 Ω Ω (D) 8 Ω Ω 4Ω 4Ω G 8Ω 4Ω x 6. An arrangement of three metallic conductors is shown. What is the magnitude of charge appearing on the left face of the conductor B? (A has a total charge Q 1 and C has a total charge Q ) zero Q1 Q (D) Q Q 1 Q 1 Q A B C FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi , Ph , , Fax

10 AITS-CRT(Set-IV)-PCM-JEE(Main)/ The potential difference (V) across the µf capacitor increases dv -1 with time, and =1Vs and dt The p.d. across the 3H inductor is 6µV 1µV 6V (D) none of these. dv = Vs dt - at particular instant. 1A Ω + - µ F 3H i 8. The rate of flow of glycerin of density ρ through conical section of a pipe, if the area of crosssectional of its ends are A 1 and A and pressure drop across its length be P, is given by AA P ρα ( 1 A ) 1 P ρα ( 1 A ) (D) AA P ρα ( 1 A ) 1 AA P 3ρ Α ( 1 A ) 1 9. Consider a particle of mass m 0 enclosed by a closed imaginary surface S. Let E be the gravitational field intensity due to m 0 at the surface element ds directed as outward normal to it. The surface integral of the gravitational field over S is m 0 G 4πm 0 G mg 0 (D) None of these 4π 30. For an adiabatic compression (for an ideal gas) the quantity PV increases decreases remains constant (D) depends on γ FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi , Ph , , Fax

11 11 AITS-CRT(Set-IV)-PCM-JEE(Main)/13 Chemistry PART II Straight bjective Type This section contains 30 multiple choice questions numbered 1 to 30. Each question has 4 choices,, and (D), out of which NLY NE is correct. 1. In metal carbonyls the C bond length Decreases from double bond length to triple bond length Increases from triple bond length to double bond length Remain as triple bond length (D) Can not be predict. In the process of extraction of Al from bauxite coke powder is spreaded over the molten electrolyte to: Prevent the loss of heat by radiation from the surface Prevent the corrosion of graphite anode Prevent oxidation of molten aluminium by air (D) Both and 3. For the reaction: HgCl( s) + H( g) Hg ( ) + HCl( aq. ); the correct representation of the cell and the thermodynamic properties G and H at 98 K respectively are: (Given E 98 = V and temperature coefficient = V/K) Pt H (g, 1 atm) HCl(aq) Hg Cl (g) Hg(liq); 1 1 G = 51.8 kjmol, H = 69 kj mol Pt H (g, 1 atm) HCl(aq) Hg Cl (g) Hg(liq); 1 1 G = 5.9 kjmol, H = 34.5 kj mol Hg(liq) Hg Cl (g) HCl(aq) H (g, 1 atm) Pt; 1 1 G = 51.8 kjmol, H = 69 kj mol (D) Hg(liq) Hg Cl (g) HCl(aq) H (g, 1 atm) Pt; 1 1 G = kjmol, H = 69 kj mol FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi , Ph , , Fax

12 AITS-CRT(Set-IV)-PCM-JEE(Main)/ The decomposition of 3 to occurs by the following mechanism K1 Mg+ g g+ g+ Mg; E (i) ( ) ( ) ( ) ( ) ( ) (ii) ( ) + + ( ) + K ( ) ( ) + ( ) (iii) ( g) + K3 ( g) ( g ); E 3 a1 g g M g M g g ; K 3 a 3 a3 Where M is catalyst If K 3 [ 3 ] >> K [ ][M], then the activation energy of the overall reaction is: EaE 1 a Ea + E 3 a E 1 a Ea E (D) a 5. In the following reaction: E a 1 S Ac /NaAc heat [ ] X ; X is...? Major (D) S Ac S CCH 3 S 6. Which of the following statement is correct? Anti-conformer of BrCH CH Br is more stable than its Gauche conformer N H is less basic than N H Gauche conformer of butane dioic acid is more stable than its anti-conformer at high ph. (D) and are correct FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi , Ph , , Fax

13 13 AITS-CRT(Set-IV)-PCM-JEE(Main)/13 7. The Major product formed in the reaction of 1,5-cyclooctadiene with 0.5 eq. of diborane is: BH B B H (D) H B H BH 8. Buta-1,3-diene on heating with maleic and hydride would give H H H H (D) H H H H 9. Which of the following is not the characteristic of interhalogen compounds? They are more reactive than halogens They are quite unstable but none of them is explosive They are covalent in nature (D) They have low b.p. and high volatility 10. Which of the following has best leaving group ability? CH3C CH3 H (D) SCF3 11. Number of π-bonds in cyclic trimer of solid S 3 is: (D) 7 FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi , Ph , , Fax

14 AITS-CRT(Set-IV)-PCM-JEE(Main)/ What is the probability density of the electron cloud at the nucleus of hydrogen. Given 1 r/a 0 1s e ψ = 3 πa 1 πa πa 1 (D) Which one is the most likely structure of CrCl 3.6H, if 1 of total chlorine of the compound is 3 precipitated by adding AgN 3 of its aqueous solution? CrCl 3.6H [Cr(H ) 3 Cl 3 ].3H [CrCl (H ) 4 ]Cl.H (D) [CrCl(H ) 5 ]Cl.H 14. In the equation: 4M + 8CN + H + 4[ M(CN) ] + 4H Identify the metal M. Cu Fe Au (D) Zn 15. Which one has largest number of isomers? [Co(en) Cl ] + [Co(NH 3 ) 5 Cl] + [Ir(PR 3 ) (H )] + : (R = alkyl) (D) [Ru(NH 3 ) 4 Cl ] The compound (SiH 3 ) 3 N is expected to be: Pyramidal and more basic than (CH 3 ) 3 N Planar and less basic than (CH 3 ) 3 N Pyramidal and less basic than (CH 3 ) 3 N (D) Planar and more basic than (CH 3 ) 3 N 17. Which of the following combination of salt and solvent is correct, (such that salt is soluble in the solvent): Salt Solvent (a) BeS 4 H (b) BaS 4 H (c) Be(H) aq. NaH (d) Ba(H) aq. NaH a and b b and c a and c (D) b and d FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi , Ph , , Fax

15 15 AITS-CRT(Set-IV)-PCM-JEE(Main)/ van-der Waal s constant b for Ar is m 3 /mol. The molecular diameter of Ar is nm nm mm (D) nm 19. Identify A, B and C from the following reactions: Na + C NaC3 + ( A) Na + ( B) NaC3 + ( A) K + ( B) KC3 + ( A) Na3 + Cl + carbon ( B) + NaCl C + NaCl + C NaHC + white sublimative ( ) 3 AgCl + ( C) + H soluble complex of Ag A = C; B = ; C = PH 3 A = ; B = C; C = NH 3 A = ; B = C ; C = NH 3 (D) A = C; B = C ; C = NH 3 0. The Bronsted acidity of boron hydrides follows the order: B H 6 > B 4 H 10 > B 5 H 9 > B 10 H 14 B H 6 = B 4 H 10 > B 5 H 9 = B 10 H 14 B 10 H 14 > B 5 H 9 > B 4 H 10 > B H 6 (D) B 5 H 9 > B 4 H 10 > B H 6 > B 10 H The change in entropy when two moles of Ar gas are heated at constant volume from 300 K to 500 K is: J/K mol J/K-mol 6.37 J/K mol (D) 1.74 J/K mol FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi , Ph , , Fax

16 AITS-CRT(Set-IV)-PCM-JEE(Main)/ What is the product X of the following reaction? Me + H [ X] Me Me Me H Me Me H Me Me (D) Me Me H H 3. The diene which undergo Diels-Alder reaction with maleic anhydride is: (D) FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi , Ph , , Fax

17 17 AITS-CRT(Set-IV)-PCM-JEE(Main)/13 4. o /490 C (D) 5. The decreasing order of reactivity of the following compounds towards electrophiles is.. N S N H (I) (II) (III) II > I > III III > I > II II > III > I (D) I > II > III 6. What are the correct stereochemical notations of the compound H CH 3 H Z, 4R E, 4R Z, 4S (D) E, 4S FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi , Ph , , Fax

18 AITS-CRT(Set-IV)-PCM-JEE(Main)/ For the aldotetroes I, II and III, which of the given statements is true? CH CH CH H H H H H H CH H (I) CH H (II) CH H (III) I and II are diastereomers while II and III are enantiomers. nly I is HI 4 cleavable I and III are D-sugars (D) All above are true 8. xymercuration-demercuration reaction of 1-methyl cyclohexene gives: cis--methylcyclohexanol trans--methylcyclohexanol 1-methylcyclohexanol (D) mixture of cis and trans--methylcyclohexanol 9. Among the following the acid which undergoes fastest decarboxylation: Ph CH PhCH (D) Ph H CH Ph CH 30. Lithium dialkyl amide base on reaction with cyclohexanone, abstracts: axial H preferentially equatorial H preferentially any of the equatorial and axial H, non preferentially (D) neither axial nor equatorial H FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi , Ph , , Fax

19 19 AITS-CRT(Set-IV)-PCM-JEE(Main)/13 Mathematics PART III SECTIN A Straight bjective Type This section contains 30 multiple choice questions numbered 1 to 30. Each question has 4 choices,, and (D), out of which NLY NE is correct. 1. Let R = {(x, y) : x, y R, x + y 4 5}, R' = (x,y): x,y R,y x 9, then Dom (R R ) = { 4, 4} Range (R R ) = [0, 4] Range (R R ) = [0, 5] (D) R R does not define a function. If z 1 and z are any two complex numbers, then which of the following is true? z 1 + z = z 1 + z z 1 z = z 1 z z 1 + z z 1 + z (D) z 1 z z 1 z 3. If minimum value of f(x) = (x + bx + c ) is greater than the maximum value of g(x) = x cx + b, then (x R) b c > 3 c b > 1< c < b (D) no real values of b and c exist 4. Let x be an irrational, then lim lim [ cos(n! x) ] m m n π equals (D) indeterminate The angle of intersection of the normals at the point, of the curves x y = 8 and 9x + 5y = 5 is π π (D) π FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi , Ph , , Fax

20 AITS-CRT(Set-IV)-PCM-JEE(Main)/ (x 1)dx is equal to x (x +α x+ 1)(x +β x+ 1) x +α x+ 1+ x +β x+ 1 log + c x log x +α x + 1 x +β x c x +α x+ 1 x +β x+ 1 log + c x (D) none of these 7. Suppose values taken by a variable X are such that a x i b, where x i denotes the value of X in the i th case for i = 1,, 3. n, then a Var(X) b a Var(X) b a 4 Var(X) (D) (b a) Var(X) 8. If sin 1 x + sin 1 y + sin 1 z = π, then x 4 + y 4 + z 4 + 4x y z = k[x y + y z + z x ], where k is equal to 1 4 (D) none of these 9. If z = Max. { z, z + }, then z+ z = 1 z+ z = z+ z = (D) none of these 10. The value of a for which the system of equations a 3 x + (a + 1) 3 y + (a + ) 3 z = 0 ax + (a + 1)y + (a + )z = 0 x + y + z = 0, has a non zero solution is (D) none of these 11. If A, B and C are three square matrices of the same size such that B = CAC 1, then CA 3 C 1 is equal to B B B 3 (D) B 9 1. In a certain test, there are n questions. In this test, r students gave wrong answers to at least (n r) questions, where r = 0, 1,,.. n. If the total number of wrong answer is 4095, then the value of n is (D) 15 FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi , Ph , , Fax

21 1 AITS-CRT(Set-IV)-PCM-JEE(Main)/ If a, b, c are in A.P. p, q, r are in H.P. and ap, bq, cr are in G.P. then a c c + a a c c a b q q + b (D) b a q p p r + r p is equal to 14. The function f(x) = p[x + 1] q[x 1], where [x] is the greatest integer function is continuous at x = 1, if p q = 0 p + q = 0 p = 0 (D) q = If f (x) = g(x)(x a), where g(a) 0 and g(x) is continuous at x = a, then f is increasing in the nbd of a if g(a) > 0 and f is decreasing in the nbd of a if g(a) < 0 f is increasing in the nbd of a if g(a) < 0 f is decreasing in the nbd of a if g(a) > 0 (D) f is increasing in the nbd of a if g(a) < 0 and f is decreasing in the nbd of a if g(a) > Rolle s Theorem holds for the function f(x) = x 3 + bx + cx, 1 x at the point 4, 3 and c are b = 8, c = 5 b = 5, c = 8 b = 5, c = 8 (D) b = 5, c = 8 the value of b 17. If xdx π = then the value of (x + a )(x + b )(x + c ) (a + b)(b + c)(c + a) 0 π π 60 0 dx is (x + 4)(x + 9) 0 40 π (D) 80 π 18. The area of the region lying inside x + (y 1) = 1 and outside c x + y = c, where c = ( 1) is π 1 π 1 (4 ) + (4 + ) 4 4 π 1 (4 + ) + (D) none of these 4 FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi , Ph , , Fax

22 AITS-CRT(Set-IV)-PCM-JEE(Main)/ If for the differential equation given by y x y' = +φ, the general solution is x y x y y x x y =, then log cx x φ y is x y (D) y x 0. If θ is the angle subtended by the circle S = x + y + gx + fy + c = 0 at a point (x 1, y 1 ) outside the circle and S1 = x1 + y1 + gx1+ fy1+ c, then cos θ =? S1 + c g f S1 + c+ g f S1 c+ g + f S1 c+ g f S1 c+ g + f S1 c+ g + f (D) S + c g + f S + c+ g f 1 1. The equation of the parabola whose focus is the point (0, 0) and the tangent at the vertex is x y + 1 = 0, is x + y xy 4x + 4y 4 = 0 x + y xy + 4x 4y 4 = 0 x + y + xy 4x + 4y 4 = 0 (D) x + y + xy 4x 4y + 4 = 0 1. The locus of the middle points of the portion of the tangents of the ellipse between the axis is the curve x y a b + = 4 + = 4 a b x y a x + b y = 4 (D) b x + a y = 4 x a y + = 1, included b x y 3. If PQ is a double ordinate of the hyperbola = 1, such that PQ is an equilateral triangle, a b being the centre of the hyperbola. Then the eccentricity e of the hyperbola satisfies 1< e < e = e = (D) e > 3 FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi , Ph , , Fax

23 3 AITS-CRT(Set-IV)-PCM-JEE(Main)/13 4. If the vector aandb are perpendicular to each other, then a vector V satisfying the equations V.a = 0, V.b = 1 and [Vab] = 1, is b (a b) b (a b) + + b a b b a b b/ b (D) none of these (a b)/ a b in terms of a and b 5. A problem in mathematics is given to 3 students whose chances of solving individually are 1 1 1, and. The probability that the problem will be solved at least by one is (D) The mean and S.D. of a binomial variate X are 4 and 3 respectively. Then P(X 1) is equal to (D) π 7. If sin θ=, 0 13 <θ< and 3 3π cos φ=,, 5 π<φ< then sin(θ + φ) will be (D) FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi , Ph , , Fax

24 AITS-CRT(Set-IV)-PCM-JEE(Main)/ The general value of θ obtained from the equation cos θ = sinα, is ( n ) π π θ= α θ = nπ± α n n π+ ( 1) π π α θ= (D) θ= nπ± 4 9. If two towers of heights h 1 and h subtend angles 60º and 30º respectively at the mid-point of the line joining their feet, then h 1 : h is equal to 1 : 1 : 3 : 1 (D) 3 : If a, b, c, d, e and f are G.P. then the value of x and y y and z a d x b e y c f z depends on x and z (D) independent of x, y and z FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi , Ph , , Fax